The Hammers more than held their own but were undone by two quickfire late goals, with Christian Benteke netting from the penalty spot and Charles N'Zogbia scoring a fine free-kick, before Ashley Westwood's own-goal gave them false hope at the death.
Allardyce said: "I think anybody who watched that performance - apart from the Aston Villa fans - knew that we deserved something out of the game.
"The sad thing is after dominating the match for so long - particularly in the second half - and not converting the chances into goals, we paid a heavy price for that.
"We gave a free-kick away and Charles N'Zogbia scored from it and we gave a penalty away and they scored from it.
"Apart from Jussi Jaaskelainen spilling the early shot, Aston Villa, in terms of chances created, have contributed nothing. In terms of our chances we were really just waiting to see what Villa had to throw at us.
"We knew they'd come out of the blocks in the first half. We contained that really well and in the second half we knew we were going to go and go at them.
"We got at them and created chance after chance after chance and when you create that many chances and don't put the ball in the back of the net you can pay a heavy price in this league. We dominated the second half and ended up losing 2-1.
"Even right at the very end their goalkeeper was the hero for them. He was the man that saved them and got them the win and we are bitterly disappointed that we haven't got at least a point out of the game."
Defender Joey Brien will miss West Ham's warm weather break in Dubai this week after suffering a thigh injury.